Heute mal ein bisschen climatology! The following question, funny and useless, is dedicated to my friend A. Wirth, who has left pure mathematics in order to use his mind for applied sciences like oceanography and meteorology ;-)

Exercise: Suppose that the earth is a perfect ball and that the temperature on the earth's surface is a continuous function. Prove that there are infinitely many pairwise disjoint sets {A,B} with A and B points on the earth surface such that the temperature in A and B is the same and such that the distance between A and B is 1000 km.